Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day, informal meeting of mathematicians from the University of Illinois, Purdue University and nearby universities, with interests in algebra, geometry and combinatorics (widely interpreted).Further details will be posted here as they become available. Or you may contact the University of Illinois organizers Hal Schenck and Alexander Yong, or the Purdue organizers Uli Walther and Saugata Basu .
Nero Budur (Notre Dame) 9h30 - 10h30 Title: Local systems and singularities.
Abstract: The local systems on the complement of an arbitrary divisor
in a smooth complex projective variety contain a wealth of information
about the singularities of the divisor. We describe various
filtrations on local systems (Hodge, polar), their induced
stratifications on the space of unitary rank one local systems, and
their relation with the singularities of the divisor. Applications
include: some results about Hodge numbers of abelian covers, and some
results about singularity invariants (Hodge spectra, b-functions, and
topological zeta functions) for hyperplane arrangements. This surveys
joint work with various people.
Rinat Kedem (UIUC) 11h - 12hTitle: Discrete integrable evolutions and noncommutative cluster algebras
Abstract: I will explain to to generalize the notion of a cluster mutation to
the non-commutative case, by using what we know about cluster algebras related
to integrable discrete evolutions. Special cases of noncommutativity include,
but are more general than, quantum cluster algebras related to canonical basis
[c.f. Berenstein, Zelevinsky].
Ben Howard (Michigan) 14h - 15h
Title: The relations among invariants of ordered points on the projective line
Abstract: We consider the coordinate rings of GIT quotients of n points on the
Peter Scheiblechner (Purdue) 16h - 17hTitle: On the Computation of the Cohomology of Complex Algebraic Varieties
Abstract: We consider the algorithmic problem of computing the (singular) cohomology
of a complex algebraic variety from a set of defining equations.
The best known algorithms solving this problem run in double exponential
time. We report on partial results towards single exponential time algorithms, in particular
concerning the zeroth cohomology and the smooth projective case. We shall give some
ideas about these algorithms, describe how good degree bounds yield efficient algorithms,
and what is used to prove such bounds.We have reserved a block of rooms at the Union Club Hotel which is conveniently located on campus and a two-minutes walk to the Mathematics department.
here for dining options in the Lafayette-West Lafayette area.
We will go for dinner on Sat evening at 6.30 to the Nine Irish Brothers.
Parking is free on Saturdays on campus. The most convenient parking garage is on N. University street adjacent to the Math building.